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Code Generation aims at generating relevant code fragments according to given natural language descriptions. In the process of software development, there exist a large number of repetitive and low-tech code writing tasks, so code generation has received a lot of attention among academia and industry for assisting developers in coding. In fact, it has also been one of the key concerns in the field of software engineering to make machines understand users' requirements and write programs on their own. The recent development of deep learning techniques especially pre-training models make the code generation task achieve promising performance. In this paper, we systematically review the current work on deep learning-based code generation and classify the current deep learning-based code generation methods into three categories: methods based on code features, methods incorporated with retrieval, and methods incorporated with post-processing. The first category refers to the methods that use deep learning algorithms for code generation based on code features, and the second and third categories of methods improve the performance of the methods in the first category. In this paper, the existing research results of each category of methods are systematically reviewed, summarized and commented. The paper then summarizes and analyzes the corpus and the popular evaluation metrics used in the existing code generation work. Finally, the paper summarizes the overall literature review and provides a prospect on future research directions worthy of attention.